How do I solve this?

1. Show that f, a bounded function on [a, b] is integrable on [a, b] if and only if, for every ( > 0 there is a partition P of [a, b] so that UP ( f ) - LP (f ) SE. 2. Show that ( t + 1 1 1 ) 2 dt = 2.1-2 3 (2 + (x]), for all real x. 3. Let f(x) be a nonnegative, integrable function on [0, 1] with f(0) = f(1) = 0. Suppose that f is differentiable at every point of [0, 1] and er f'(x) is integrable on [0, 1]. Show that 02 eff'(x)dx > -e / f(x)dx. 0